The present invention relates to measurement, and, more particularly, to a system and method for measuring exponential decay time constants and parameters derivable therefrom. While the present invention has many applications, it has particular application to the measurement of oxygen concentration, for example, in blood, based on luminescence quenching.
Oxygen concentration in various solutions, e.g., blood, can be measured by determining a fluorescence decay time constant. A fluorescent dye, protected as appropriate, can be dissolved in a sample solution. Fluorescence is initiated by stimulating the dissolved dye with light of an appropriate wavelength. In a case where the stimulus is abruptly terminated, the fluorescence does not end instantaneously. Rather, the fluorescence decays according to an exponential decay function.
In such a dyed sample solution, fluorescence is quenched by the presence of oxygen so that the intensity and duration of the fluorescence are decreased as a function of oxygen concentration. Theoretically, oxygen concentration could be measured as a function of either intensity or duration. However, intensity is difficult to work with as it varies with many system variables such as temperature, stimulus intensity, opto-mechanical coupling, fiber bending losses, etc.
Since fluorescent decay can be characterized exponentially, the exponential time constant, .tau., of such fluorescent decay can be used as an amplitude independent measure of oxygen concentration. The time constant for a sample can be determined directly by stimulating and then abruptly terminating stimulation of a dyed sample, and then finding a time interval over which intensity decreases by a factor of 1/e, about 63%. Similarly, the percent change over a fixed time interval can be used to determine the time constant. Due to the pervasive presence of noise, such direct methods do not afford very high precision unless averaging is performed over many measurements. Thus, a periodic, rather than a one-shot, stimulus is usually preferred.
For example, in a pulse method, a sample is stimulated with a pulse train to yield a periodic response signal. The average delay of the response with respect to the stimulus is used as a measure of oxygen concentration. One major disadvantage of the pulse method is the difficulty of producing sharply defined stimulus pulses. Generally available light sources yield pulses several nanoseconds in duration, which is often already a substantial fraction of fluorescent lifetimes.
While it is possible to use iterative convolution to parcel out the effect of the extended pulse duration from the exponential decay, this requires very carefully controlled pulse shapes. The mathematics involved in iterative convolution are even more complicated in cases where the decays overlap due to a high-frequency stimulus signal. Another solution is to use lasers with picosecond pulse width, but such lasers are not widely available due to cost and technical considerations.
A phase-shift method can be used which avoids some of the disadvantages of the pulse method. In a typical application of the phase-shift method, the sample is stimulated with sinusoidally modulated light. The output in such a case is the convolution of the stimulus sine wave and the system exponential function, which is also a sine wave but with a shifted phase. Thus, the time constant can still be determined indirectly from the phase of the response signal relative to the stimulus signal. Phase can be readily determined by using a variety of phase detectors.
The phase-shift method has several advantages. Short, even sub-nanosecond, time constants can be easily measured. Data acquisition is relatively rapid, which is generally convenient and critical where the parameter of interest can change quickly.
Another important advantage of the phase-shift method is that it is readily adapted to more complex sample analysis where multiple time constants can be superimposed on each other. In theory, it is possible to record directly the individual time constant of each fluorescent source in a mixture using the phase-shift method.
There remain two significant disadvantages to the phase-shift approach. In the first place, phase can be difficult to measure with great precision. Phase detectors can be sensitive to amplitude effects, and thus distorted readings are difficult to avoid.
In the second place, the sensitivity of systems implementing the phase-shift method generally vary as a function of phase shift. In other words, outside a narrow range of phases, the signal-to-noise ratio is below the maximum achievable.
In some systems, provision is made for multiple frequencies for the stimulus signal. This multiplies the range of sample characteristics that can be detected using optimal phase ranges. However, the selection of the alternate frequencies is an inconvenience to the user, perhaps requiring a succession of useless measurements to be made before the desired one is achieved. In the meantime, validity erodes as sample parameters can change. Futhermore, this approach still does not provide continuous optimal sensitivity.
This limitation in sensitivity can be very significant in systems which, because of limited stimulus intensity or sample responsiveness, the desired signal is of comparable intensity to noise. In these cases it may not be possible to obtain a valid measurement outside of the maximum sensitivity range of the instrument. Thus, a phase-shift system would not be able to provide valid measurements over a continuous extended range.
Given the disadvantages of available methods as applied to oxygen measurements as well as a broad range of applications involving exponential decay, what is needed is an improved system and method for determining exponential decay time constants. The system should be convenient to use and provide optimal sensitivity over an extended and continuous measurement range. In addition, the measurement approach should be susceptible to convenient and precise readout.